The Gross Zagier Formula on Shimura Curves is popular PDF and ePub book, written by Xinyi Yuan in 2013, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Gross Zagier Formula on Shimura Curves can be Read Online from any device for your convenience.
The Gross Zagier Formula on Shimura Curves Book PDF Summary
This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.
Detail Book of The Gross Zagier Formula on Shimura Curves PDF
- Author : Xinyi Yuan
- Release : 21 September 2024
- Publisher : Princeton University Press
- ISBN : 9780691155920
- Genre : Mathematics
- Total Page : 266 pages
- Language : English
- PDF File Size : 14,8 Mb
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